Résumé

We investigate the simultaneous production planning and quality control problem for an unreliable single machine manufacturing system responding to a single product type demand. The machine is subject to deteriorations, and their effect is observed mainly on the rate of defectives, which increases continuously over time. Due to the uncertainty caused by failures, the machine may not meet long-term demand, and an overhaul can be conducted in order to counter the effect of the deterioration. The main objective of this study is to simultaneously determine the optimal production plan and overhaul schedule for the analyzed manufacturing system, in order to minimize the total cost, comprising the inventory, backlog, repair and overhaul cost, over an infinite planning horizon. A stochastic dynamic programming model is proposed, in which a numerical scheme is adopted to solve the optimality condition equations. It is observed that the optimal control policy is described by a machine deterioration-dependent hedging point policy (MDDHPP). To accurately approximate the related control parameters, a simulation optimization approach based on design of experiments, simulation modeling and response surface methodology is applied. The results obtained provide a better understanding about the influence of the deterioration of quality in the production and overhaul policies. A numerical example and an extensive sensitivity analysis are conducted, and show the robust behavior and usefulness of the policy obtained.